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For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is 3d/4, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C0) is given by relation -

1. C' = (3 + K)/(4K) C0
2. C' = (4 + K)/3 C0
3. C' = (4K)/(K + 3) C0
4. C' = 4/(3 + K) C0

Correct answer: C' = (4K)/(K + 3) C0

Solution

The correct option is derived from the formula for capacitance with a dielectric, considering the effective area and thickness of the dielectric slab. By substituting the values for the dielectric constant and the dimensions of the capacitor, the relationship simplifies to C' = (4K)/(K + 3) C0, accurately reflecting how the dielectric alters the capacitance.

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